R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(3922,3759,4138,4634,3995,4308,4143,4429,5219,4929,5755,5592,4163,4962,5208,4755,4491,5732,5731,5040,6102,4904,5369,5578,4619,4731,5011,5299,4146,4625,4736,4219,5116,4205,4121,5103,4300,4578,3809,5526,4247,3830,4394,4826,4409,4569,4106,4794,3914,3793,4405,4022,4100,4788,3163,3585,3903,4178,3863,4187)
> x <- c(6.7,6.5,6.2,6.2,6.5,6.8,6.8,6.5,5.9,5.5,5.6,6,6.3,6.2,5.6,5.4,5.7,5.9,6.2,6.3,6.1,5.9,5.9,5.7,5.9,6.1,6.1,6.5,6.8,6.8,6.9,6.9,6.8,6.6,6.5,6.5,6.5,6.7,7,7.3,7.5,7.5,7.5,7.3,7.1,6.9,7,7.1,7.2,7.1,6.8,6.9,6.9,7.3,7.4,7.2,6.9,6.8,7.1,7.4)
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> n <- length(x)
> c <- array(NA,dim=c(401))
> l <- array(NA,dim=c(401))
> mx <- 0
> mxli <- -999
> for (i in 1:401)
+ {
+ l[i] <- (i-201)/100
+ if (l[i] != 0)
+ {
+ x1 <- (x^l[i] - 1) / l[i]
+ } else {
+ x1 <- log(x)
+ }
+ c[i] <- cor(x1,y)
+ if (mx < abs(c[i]))
+ {
+ mx <- abs(c[i])
+ mxli <- l[i]
+ }
+ }
> c
  [1] -0.5784753 -0.5784975 -0.5785194 -0.5785412 -0.5785629 -0.5785843
  [7] -0.5786056 -0.5786266 -0.5786475 -0.5786682 -0.5786888 -0.5787091
 [13] -0.5787293 -0.5787493 -0.5787691 -0.5787888 -0.5788082 -0.5788275
 [19] -0.5788466 -0.5788655 -0.5788843 -0.5789028 -0.5789212 -0.5789394
 [25] -0.5789574 -0.5789753 -0.5789929 -0.5790104 -0.5790277 -0.5790448
 [31] -0.5790617 -0.5790785 -0.5790951 -0.5791115 -0.5791277 -0.5791437
 [37] -0.5791596 -0.5791753 -0.5791908 -0.5792061 -0.5792212 -0.5792362
 [43] -0.5792509 -0.5792655 -0.5792799 -0.5792942 -0.5793082 -0.5793221
 [49] -0.5793358 -0.5793493 -0.5793626 -0.5793758 -0.5793888 -0.5794016
 [55] -0.5794142 -0.5794266 -0.5794388 -0.5794509 -0.5794628 -0.5794745
 [61] -0.5794860 -0.5794974 -0.5795086 -0.5795196 -0.5795304 -0.5795410
 [67] -0.5795514 -0.5795617 -0.5795718 -0.5795817 -0.5795914 -0.5796010
 [73] -0.5796104 -0.5796196 -0.5796286 -0.5796374 -0.5796460 -0.5796545
 [79] -0.5796628 -0.5796709 -0.5796788 -0.5796866 -0.5796942 -0.5797015
 [85] -0.5797088 -0.5797158 -0.5797226 -0.5797293 -0.5797358 -0.5797421
 [91] -0.5797482 -0.5797542 -0.5797600 -0.5797655 -0.5797710 -0.5797762
 [97] -0.5797812 -0.5797861 -0.5797908 -0.5797953 -0.5797997 -0.5798038
[103] -0.5798078 -0.5798116 -0.5798152 -0.5798186 -0.5798219 -0.5798250
[109] -0.5798279 -0.5798306 -0.5798331 -0.5798355 -0.5798377 -0.5798397
[115] -0.5798415 -0.5798431 -0.5798446 -0.5798459 -0.5798470 -0.5798479
[121] -0.5798487 -0.5798492 -0.5798496 -0.5798499 -0.5798499 -0.5798497
[127] -0.5798494 -0.5798489 -0.5798482 -0.5798474 -0.5798463 -0.5798451
[133] -0.5798437 -0.5798421 -0.5798404 -0.5798385 -0.5798363 -0.5798341
[139] -0.5798316 -0.5798289 -0.5798261 -0.5798231 -0.5798199 -0.5798166
[145] -0.5798130 -0.5798093 -0.5798054 -0.5798014 -0.5797971 -0.5797927
[151] -0.5797881 -0.5797833 -0.5797783 -0.5797732 -0.5797679 -0.5797624
[157] -0.5797567 -0.5797509 -0.5797449 -0.5797387 -0.5797323 -0.5797257
[163] -0.5797190 -0.5797121 -0.5797050 -0.5796977 -0.5796903 -0.5796826
[169] -0.5796748 -0.5796669 -0.5796587 -0.5796504 -0.5796419 -0.5796332
[175] -0.5796243 -0.5796153 -0.5796061 -0.5795967 -0.5795872 -0.5795774
[181] -0.5795675 -0.5795574 -0.5795471 -0.5795367 -0.5795261 -0.5795153
[187] -0.5795043 -0.5794931 -0.5794818 -0.5794703 -0.5794586 -0.5794468
[193] -0.5794347 -0.5794225 -0.5794102 -0.5793976 -0.5793849 -0.5793720
[199] -0.5793589 -0.5793456 -0.5793322 -0.5793186 -0.5793048 -0.5792909
[205] -0.5792767 -0.5792624 -0.5792479 -0.5792333 -0.5792184 -0.5792034
[211] -0.5791883 -0.5791729 -0.5791574 -0.5791417 -0.5791258 -0.5791097
[217] -0.5790935 -0.5790771 -0.5790606 -0.5790438 -0.5790269 -0.5790098
[223] -0.5789925 -0.5789751 -0.5789575 -0.5789397 -0.5789217 -0.5789036
[229] -0.5788853 -0.5788668 -0.5788481 -0.5788293 -0.5788103 -0.5787911
[235] -0.5787718 -0.5787523 -0.5787326 -0.5787127 -0.5786927 -0.5786725
[241] -0.5786521 -0.5786315 -0.5786108 -0.5785899 -0.5785688 -0.5785476
[247] -0.5785262 -0.5785046 -0.5784828 -0.5784609 -0.5784388 -0.5784165
[253] -0.5783941 -0.5783715 -0.5783487 -0.5783257 -0.5783026 -0.5782793
[259] -0.5782559 -0.5782322 -0.5782084 -0.5781844 -0.5781603 -0.5781360
[265] -0.5781115 -0.5780868 -0.5780620 -0.5780370 -0.5780118 -0.5779865
[271] -0.5779609 -0.5779353 -0.5779094 -0.5778834 -0.5778572 -0.5778308
[277] -0.5778043 -0.5777776 -0.5777508 -0.5777237 -0.5776965 -0.5776691
[283] -0.5776416 -0.5776139 -0.5775860 -0.5775580 -0.5775298 -0.5775014
[289] -0.5774728 -0.5774441 -0.5774152 -0.5773862 -0.5773569 -0.5773276
[295] -0.5772980 -0.5772683 -0.5772384 -0.5772083 -0.5771781 -0.5771477
[301] -0.5771171 -0.5770864 -0.5770555 -0.5770245 -0.5769932 -0.5769618
[307] -0.5769303 -0.5768986 -0.5768667 -0.5768346 -0.5768024 -0.5767700
[313] -0.5767374 -0.5767047 -0.5766718 -0.5766388 -0.5766056 -0.5765722
[319] -0.5765386 -0.5765049 -0.5764711 -0.5764370 -0.5764028 -0.5763684
[325] -0.5763339 -0.5762992 -0.5762643 -0.5762293 -0.5761941 -0.5761588
[331] -0.5761233 -0.5760876 -0.5760517 -0.5760157 -0.5759795 -0.5759432
[337] -0.5759067 -0.5758701 -0.5758332 -0.5757962 -0.5757591 -0.5757218
[343] -0.5756843 -0.5756467 -0.5756089 -0.5755709 -0.5755328 -0.5754945
[349] -0.5754561 -0.5754175 -0.5753787 -0.5753398 -0.5753007 -0.5752614
[355] -0.5752220 -0.5751824 -0.5751427 -0.5751028 -0.5750627 -0.5750225
[361] -0.5749822 -0.5749416 -0.5749009 -0.5748601 -0.5748190 -0.5747779
[367] -0.5747365 -0.5746950 -0.5746534 -0.5746116 -0.5745696 -0.5745275
[373] -0.5744852 -0.5744427 -0.5744001 -0.5743574 -0.5743144 -0.5742713
[379] -0.5742281 -0.5741847 -0.5741412 -0.5740974 -0.5740536 -0.5740095
[385] -0.5739654 -0.5739210 -0.5738765 -0.5738319 -0.5737870 -0.5737421
[391] -0.5736969 -0.5736517 -0.5736062 -0.5735606 -0.5735149 -0.5734690
[397] -0.5734229 -0.5733767 -0.5733303 -0.5732838 -0.5732371
> mx
[1] 0.5798499
> mxli
[1] -0.76
> if (mxli != 0)
+ {
+ x1 <- (x^mxli - 1) / mxli
+ } else {
+ x1 <- log(x)
+ }
> r<-lm(y~x)
> se <- sqrt(var(r$residuals))
> r1 <- lm(y~x1)
> se1 <- sqrt(var(r1$residuals))
> postscript(file="/var/www/html/rcomp/tmp/1khhn1257936842.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Linearity Plot',xlab='Lambda',ylab='correlation')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2hcc41257936842.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x,y,main='Linear Fit of Original Data',xlab='x',ylab='y')
> abline(r)
> grid()
> mtext(paste('Residual Standard Deviation = ',se))
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3pwcu1257936842.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x1,y,main='Linear Fit of Transformed Data',xlab='x',ylab='y')
> abline(r1)
> grid()
> mtext(paste('Residual Standard Deviation = ',se1))
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Box-Cox Linearity Plot',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'# observations x',header=TRUE)
> a<-table.element(a,n)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'maximum correlation',header=TRUE)
> a<-table.element(a,mx)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'optimal lambda(x)',header=TRUE)
> a<-table.element(a,mxli)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Residual SD (orginial)',header=TRUE)
> a<-table.element(a,se)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Residual SD (transformed)',header=TRUE)
> a<-table.element(a,se1)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/4pq9v1257936842.tab") 
> 
> system("convert tmp/1khhn1257936842.ps tmp/1khhn1257936842.png")
> system("convert tmp/2hcc41257936842.ps tmp/2hcc41257936842.png")
> system("convert tmp/3pwcu1257936842.ps tmp/3pwcu1257936842.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.726   0.504   0.956